响应变量随机缺失的相依函数型单指标模型的k近邻估计  

k-nearest Neighbor Estimation for Dependent Function Single-indicator Models with Random Missing Response Variables

作　　者：何文然 黄振生 HE Wenran;HUANG Zhensheng(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学数学与统计学院,南京210094

出　　处：《重庆工商大学学报（自然科学版）》2023年第6期105-110,共6页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：全国统计科学研究重大项目(2018LD01).

摘　　要：针对具有α混合结构的函数型时间序列数据,当响应变量随机缺失时,利用函数型单指标模型进行统计建模,并采用k近邻方法对模型中未知参数和未知函数进行估计,与经典核方法相比,其数据适用性更强,可以提高估计效率;通过数值模拟和厄尔尼诺海平面温度数据,将k近邻方法和经典核方法进行比较,讨论k近邻方法与经典核方法对未知参数和未知函数的估计效果;从模拟结果可以看到:k近邻方法对未知参数和未知函数的估计精度以及随样本增加的改善效果要优于经典核方法,在真实数据分析中,k近邻对真实数据的精度拟合以及趋势拟合都表现优异;这些结果表明:在响应变量随机缺失的时间序列单指标模型中,采用k近邻方法对未知参数和未知函数进行估计,在精度上要优于经典核方法,同时在真实数据分析中,相比经典核方法,k近邻方法能更好地拟合数据。For functional time series data withα-mixed structure,when the response variables are randomly missing,the functional single indicator model is used for statistical modeling,and the k-nearest neighbor method is used to estimate the unknown parameters and unknown functions in the model.Compared with the classical kernel method,the method proposed in this paper has better data applicability and can improve the estimation efficiency.The k-nearest neighbor method was compared with the classical kernel method through numerical simulations and El Ni o sea level temperature data to discuss the estimation effects of the k-nearest neighbor method and the classical kernel method on the unknown parameters and unknown functions.From the simulation results,it can be seen that the k-nearest neighbor method outperformed the classical kernel method in terms of accuracy of estimation of unknown parameters and unknown functions as well as improvement with increasing samples.Moreover,in the analysis of real data,the k-nearest neighbor method performed well in the accuracy fitting and trend fitting of real data.These results show that the k-nearest neighbor method is superior to the classical kernel method in terms of accuracy in estimating the unknown parameters and unknown functions in a single indicator model of a time series with random missing response variables.Meanwhile,in the real data analysis,the k-nearest neighbor method can better fit the data than the classical kernel method.

关 键 词：函数型单指标模型 α混合 k近邻估计 随机缺失 

分 类 号：O212.7[理学—概率论与数理统计]